Operator Algebra Seminar

Speaker:  Søren Knudby (WWU Münster)

Title: A complete characterization of connected Lie groups with the Approximation Property

Abstract : The Approximation Property (AP) is the group analogue of the operator approximation property for C*-algebras. In 2011, Lafforgue and de la Salle showed that SL(3,Z) and SL(3,R) do not have the AP. In 2013, Haagerup and de Laat extended the result to cover all simple Lie groups of real rank at least two. In this talk, based on joint work with Haagerup and de Laat, we further generalize the previous results to include non-simple Lie groups, thus obtaining a complete characterization of all connected Lie groups with the AP.

To this end, we introduce property (T*), a strengthening of property (T), which is a natural obstruction to the AP, and we exploit an important permanence result about property (T*).